Expert: Paul Klarreich - 1/22/2006

Question
The inverse of the following matrix can be found by performing a single row operation (once the proper 4x8 matrix has been written down). Indicate what that row operation would be (give your answer in a form such as R5 + 13 R7 or R3 - 17 R2 )

1 0 32 0
0 1  0 0
0 0  1 0
0 0  0 1

Answer
Hi, Kevin,
Your Matrix Question:  The inverse of the following matrix can be found by performing a single row operation (once the proper 4x8 matrix has been written down). Indicate what that row operation would be (give your answer in a form such as R5 + 13 R7 or R3 - 17 R2 )

VIEW THIS IN A FIXED FONT.

1  0 32  0
0  1  0  0
0  0  1  0
0  0  0  1

wants to become the unit matrix, i.e.

1  0  0  0
0  1  0  0
0  0  1  0
0  0  0  1

So we want to get rid of that 32.  We can do it by finding a row that will leave the other elements undisturbed, i.e. has zeroes in the other columns.

Row 3 has just what we want.  All we have to do is multiply row 3 by 32 and subtract it from row 1.  I suppose your notation would require us to say:

R1 = R1 - 32R3